PSN plus: Once games are free, are they free forever? [duplicate]

I know that with the Playstation plus membership, they will away free games every month and giving away different games every month. So, I were to get a free game, then a month later, that same game isn't considered a "free" ps+ game, will I still have it?

Scenario:

--June 2013-- Uncharted 3 is free for ps+ members

2 months later

--August 2013-- (Hypothetically) Uncharted 3 ISN'T offered as free for ps+ members anymore

So, if I downloaded, installed, played, etc. Uncharted 3 while it was free, will I have still owned Uncharted 3 even AFTER August 2013 when they stop offering it to ps+ members?

Also note, that during this time, my ps+ membership has NOT expired.

Yes, it will still be playable if you still have PS+ membership.

Source: own experience with Plants vs. Zombies

EDIT:

As Fluttershy says, it will only work if you "purchase" the game